login
A291563
Number of partitions of 2n into two prime parts or two nonprime parts.
2
1, 1, 1, 2, 4, 3, 4, 6, 6, 6, 8, 9, 9, 9, 11, 9, 13, 15, 10, 14, 16, 14, 16, 19, 18, 17, 21, 18, 20, 25, 18, 24, 27, 19, 26, 28, 25, 27, 32, 26, 28, 35, 29, 29, 39, 30, 32, 38, 30, 37, 41, 35, 37, 42, 38, 41, 47, 40, 40, 54, 38, 42, 53, 39, 48, 52, 46, 46
OFFSET
1,4
FORMULA
a(n) = Sum_{i=1..n} [A010051(i) = A010051(2n-i)], where [] is the Iverson bracket.
a(n) = n - A291564(n).
MAPLE
a:= n-> n-add(`if`(isprime(n+i) xor isprime(n-i), 1, 0), i=1..n-1):
seq(a(n), n=1..80); # Alois P. Heinz, Mar 05 2021
MATHEMATICA
Table[Sum[KroneckerDelta[(PrimePi[k] - PrimePi[k - 1]), (PrimePi[2 n - k] - PrimePi[2 n - 1 - k])], {k, n}], {n, 80}]
CROSSREFS
Sequence in context: A355399 A224714 A089169 * A178151 A087794 A050514
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 20 2017
STATUS
approved